The study said that exposure to innovation during childhood has "a significant causal effect on a child's propensity to become an inventor." Children who grow up in metro areas with higher patent rates are significantly more likely to become inventors.

Among the top 10 cities for children who become inventors: Madison and Milwaukee.

The study is in contrast to entrepreneurship and business startup rankings in which the state, and Milwaukee, often lag. Those measures don't place weight on patent filings, or the inventor's hometown, on which this study was based.

The study looked at a sample of people born between 1980 and 1984 and assigned each child a ZIP code based on the first tax form that claimed them as dependents. It followed those children to see how many went on to hold patents. The top cities for children's patent rates were designated by looking at the number of children who grew up to hold patents per thousand in the area. The ranking looked at the 100 metro areas with the largest populations. The top 10 are:

San Jose, Calif.

Madison

Minneapolis, Minn.

San Francisco

Detroit

Boston

Allentown, Pa.

Milwaukee

Manchester, N.H.

Newark, N.J.

Nearly five kids per 1,000 from Madison become inventors and just under four per 1,000 from Milwaukee do so, according to the study.

The team of economists behind the research includes Milwaukee-raised Raj Chetty, a professor at Stanford University.

Raj Chetty, who grew up in Milwaukee, is a professor of economics at Stanford University.(Photo: Tsar Fedorsky for Home Front Communications)

With some exceptions, the areas where children grow up to become inventors tend to have higher incomes, fewer single parent families and higher levels of absolute upward intergenerational mobility.

Not only does living in an area with higher patent rates make a child more likely to innovate, but it also affects the category for which a patent is issued. The study gave an example that for adults living in Boston, those who grew up in Silicon Valley were more likely to hold a patent in computers while people from Minneapolis were more likely to patent an invention in medical devices.

The authors note that children who grow up in the rural Midwest, Northeast and coastal California have the highest probability of becoming inventors. Children from the Southeast have the lowest probability.

'Lost Einsteins'

The authors called the study the "first comprehensive portrait of inventors in the United States." For the analysis, the researchers linked data from patent applications and grants to tax forms.

The study also examined who does not become an inventor because of life circumstances, calling these children "lost Einsteins."

Large gaps exist between children from high and below-median income families, and by race and gender. By looking at test scores from childhood, the authors determined that differences in innate ability "explain relatively little of these gaps."

"It was chilling to see that this association between test scores and invention is basically only there for kids from privileged backgrounds," said the study's lead author, Alex Bell from Harvard. "It's worrying to think that there may be a lot of kids out there who could have the skills to contribute real innovations to society, but aren't doing so because of barriers related to family background."

Exposure to innovation is important, the authors concluded.

"A lack of exposure to innovation can help explain why high-ability children in low-income families, minorities, and women are significantly less likely to become inventors," the paper said. "Importantly, such lack of exposure screens out not just marginal inventors but the 'Einsteins' who produce innovations that have the greatest impacts on society."